diff --git a/docs/getting_started/look_and_feel.md b/docs/getting_started/look_and_feel.md
index a8bfb824..1c1050e5 100644
--- a/docs/getting_started/look_and_feel.md
+++ b/docs/getting_started/look_and_feel.md
@@ -24,7 +24,7 @@ Here is a small example of operations possible on scalar quantities:
 
     static_assert(2 * m * (3 * m) == 6 * m2);
 
-    static_assert(10 * km / (5 * km) == 2 * one);
+    static_assert(10 * km / (5 * km) == 2);
 
     static_assert(1000 / (1 * s) == 1 * kHz);
     ```
@@ -51,7 +51,7 @@ Here is a small example of operations possible on scalar quantities:
 
     static_assert(2 * m * (3 * m) == 6 * m2);
 
-    static_assert(10 * km / (5 * km) == 2 * one);
+    static_assert(10 * km / (5 * km) == 2);
 
     static_assert(1000 / (1 * s) == 1 * kHz);
     ```
diff --git a/docs/users_guide/framework_basics/dimensionless_quantities.md b/docs/users_guide/framework_basics/dimensionless_quantities.md
index 33bfc9b9..3cb3d089 100644
--- a/docs/users_guide/framework_basics/dimensionless_quantities.md
+++ b/docs/users_guide/framework_basics/dimensionless_quantities.md
@@ -164,6 +164,21 @@ inline constexpr struct parts_per_million final : named_unit<"ppm", mag_ratio<1,
 inline constexpr auto ppm = parts_per_million;
 ```
 
+### Superpowers of the unit `one`
+
+Quantities of the unit `one` are the only ones that are implicitly convertible from a raw value
+and explicitly convertible to it. This property also expands to usual arithmetic operators.
+
+Thanks to the above, we can type:
+
+```cpp
+quantity<one> inc(quantity<one> q) { return q + 1; }
+void legacy(double) { /* ... */ }
+
+if (auto q = inc(42); q != 0)
+  legacy(static_cast<int>(q));
+```
+
 
 ## Angular quantities
 
diff --git a/example/kalman_filter/kalman_filter-example_1.cpp b/example/kalman_filter/kalman_filter-example_1.cpp
index 7bfb370a..da718a98 100644
--- a/example/kalman_filter/kalman_filter-example_1.cpp
+++ b/example/kalman_filter/kalman_filter-example_1.cpp
@@ -64,7 +64,7 @@ int main()
   state next = initial_guess;
   for (int index = 1; const auto& measurement : measurements) {
     const state& previous = next;
-    const quantity gain = 1. / index * one;
+    const quantity gain = 1. / index;
     const state current = state_update(previous, measurement, gain);
     next = current;
     print(index++, gain, measurement, current, next);
diff --git a/src/core/include/mp-units/framework/quantity.h b/src/core/include/mp-units/framework/quantity.h
index 279e81a7..b601c307 100644
--- a/src/core/include/mp-units/framework/quantity.h
+++ b/src/core/include/mp-units/framework/quantity.h
@@ -177,6 +177,12 @@ public:
   {
   }
 
+  template<detail::ValuePreservingTo<Rep> Value>
+    requires(unit == ::mp_units::one)
+  constexpr explicit(false) quantity(Value&& v) : numerical_value_is_an_implementation_detail_(std::forward<Value>(v))
+  {
+  }
+
   template<detail::QuantityConvertibleTo<quantity> Q>
   // NOLINTNEXTLINE(google-explicit-constructor, hicpp-explicit-conversions)
   constexpr explicit(!std::convertible_to<typename Q::rep, Rep>) quantity(const Q& q) :
@@ -199,6 +205,14 @@ public:
   quantity& operator=(const quantity&) = default;
   quantity& operator=(quantity&&) = default;
 
+  template<detail::ValuePreservingTo<Rep> Value>
+    requires(unit == ::mp_units::one)
+  constexpr quantity& operator=(Value&& v)
+  {
+    numerical_value_is_an_implementation_detail_ = std::forward<Value>(v);
+    return *this;
+  }
+
   // unit conversions
   template<detail::UnitCompatibleWith<unit, quantity_spec> ToU>
     requires detail::QuantityConvertibleTo<quantity, quantity<detail::make_reference(quantity_spec, ToU{}), Rep>>
@@ -281,6 +295,13 @@ public:
   }
 
   // conversion operators
+  template<typename V_, std::constructible_from<Rep> Value = std::remove_cvref_t<V_>>
+    requires(unit == ::mp_units::one)
+  [[nodiscard]] explicit operator V_() const& noexcept
+  {
+    return numerical_value_is_an_implementation_detail_;
+  }
+
   template<typename Q_, QuantityLike Q = std::remove_cvref_t<Q_>>
     requires detail::QuantityConvertibleTo<quantity, detail::quantity_like_type<Q>>
   [[nodiscard]] explicit(is_specialization_of<decltype(quantity_like_traits<Q>::from_numerical_value(
@@ -480,6 +501,22 @@ public:
                                 ret::reference};
   }
 
+  template<std::derived_from<quantity> Q, RepresentationOf<quantity_character::scalar> Value>
+    requires(Q::unit == ::mp_units::one) &&
+            detail::InvokeResultOf<quantity_character::scalar, std::plus<>, Rep, const Value&>
+  [[nodiscard]] friend constexpr Quantity auto operator+(const Q& lhs, const Value& rhs)
+  {
+    return lhs + ::mp_units::quantity{rhs};
+  }
+
+  template<std::derived_from<quantity> Q, RepresentationOf<quantity_character::scalar> Value>
+    requires(Q::unit == ::mp_units::one) &&
+            detail::InvokeResultOf<quantity_character::scalar, std::plus<>, Rep, const Value&>
+  [[nodiscard]] friend constexpr Quantity auto operator+(const Value& lhs, const Q& rhs)
+  {
+    return ::mp_units::quantity{lhs} + rhs;
+  }
+
   template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires detail::CommonlyInvocableQuantities<std::minus<>, quantity, quantity<R2, Rep2>>
   [[nodiscard]] friend constexpr Quantity auto operator-(const Q& lhs, const quantity<R2, Rep2>& rhs)
@@ -491,6 +528,22 @@ public:
                                 ret::reference};
   }
 
+  template<std::derived_from<quantity> Q, RepresentationOf<quantity_character::scalar> Value>
+    requires(Q::unit == ::mp_units::one) &&
+            detail::InvokeResultOf<quantity_character::scalar, std::minus<>, Rep, const Value&>
+  [[nodiscard]] friend constexpr Quantity auto operator-(const Q& lhs, const Value& rhs)
+  {
+    return lhs - ::mp_units::quantity{rhs};
+  }
+
+  template<std::derived_from<quantity> Q, RepresentationOf<quantity_character::scalar> Value>
+    requires(Q::unit == ::mp_units::one) &&
+            detail::InvokeResultOf<quantity_character::scalar, std::minus<>, Rep, const Value&>
+  [[nodiscard]] friend constexpr Quantity auto operator-(const Value& lhs, const Q& rhs)
+  {
+    return ::mp_units::quantity{lhs} - rhs;
+  }
+
   template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires(!treat_as_floating_point<Rep>) && (!treat_as_floating_point<Rep2>) &&
             detail::CommonlyInvocableQuantities<std::modulus<>, quantity, quantity<R2, Rep2>>
@@ -504,6 +557,22 @@ public:
                                 ret::reference};
   }
 
+  template<std::derived_from<quantity> Q, RepresentationOf<quantity_character::scalar> Value>
+    requires(Q::unit == ::mp_units::one) &&
+            detail::InvokeResultOf<quantity_character::scalar, std::modulus<>, Rep, const Value&>
+  [[nodiscard]] friend constexpr Quantity auto operator%(const Q& lhs, const Value& rhs)
+  {
+    return lhs % ::mp_units::quantity{rhs};
+  }
+
+  template<std::derived_from<quantity> Q, RepresentationOf<quantity_character::scalar> Value>
+    requires(Q::unit == ::mp_units::one) &&
+            detail::InvokeResultOf<quantity_character::scalar, std::modulus<>, Rep, const Value&>
+  [[nodiscard]] friend constexpr Quantity auto operator%(const Value& lhs, const Q& rhs)
+  {
+    return ::mp_units::quantity{lhs} % rhs;
+  }
+
   template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires detail::InvocableQuantities<std::multiplies<>, quantity, quantity<R2, Rep2>>
   [[nodiscard]] friend constexpr Quantity auto operator*(const Q& lhs, const quantity<R2, Rep2>& rhs)
@@ -563,6 +632,13 @@ public:
     return ct_lhs.numerical_value_ref_in(ct::unit) == ct_rhs.numerical_value_ref_in(ct::unit);
   }
 
+  template<std::derived_from<quantity> Q, RepresentationOf<quantity_character::scalar> Value>
+    requires(Q::unit == ::mp_units::one) && std::equality_comparable_with<Rep, Value>
+  [[nodiscard]] friend constexpr bool operator==(const Q& lhs, const Value& rhs)
+  {
+    return lhs.numerical_value_ref_in(unit) == rhs;
+  }
+
   template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires requires { typename std::common_type_t<quantity, quantity<R2, Rep2>>; } &&
              std::three_way_comparable<typename std::common_type_t<quantity, quantity<R2, Rep2>>::rep>
@@ -573,6 +649,13 @@ public:
     const ct ct_rhs(rhs);
     return ct_lhs.numerical_value_ref_in(ct::unit) <=> ct_rhs.numerical_value_ref_in(ct::unit);
   }
+
+  template<std::derived_from<quantity> Q, RepresentationOf<quantity_character::scalar> Value>
+    requires(Q::unit == ::mp_units::one) && std::three_way_comparable_with<Rep, Value>
+  [[nodiscard]] friend constexpr auto operator<=>(const Q& lhs, const Value& rhs)
+  {
+    return lhs.numerical_value_ref_in(unit) <=> rhs;
+  }
 };
 
 // CTAD
@@ -599,7 +682,16 @@ template<mp_units::Quantity Q1, mp_units::Quantity Q2>
     typename std::common_type_t<typename Q1::rep, typename Q2::rep>;
   }
 struct std::common_type<Q1, Q2> {
-public:
   using type = mp_units::quantity<mp_units::common_reference(Q1::reference, Q2::reference),
                                   std::common_type_t<typename Q1::rep, typename Q2::rep>>;
 };
+
+template<mp_units::Quantity Q, mp_units::RepresentationOf<mp_units::quantity_character::scalar> Value>
+  requires(Q::unit == mp_units::one) && requires { typename std::common_type_t<typename Q::rep, Value>; }
+struct std::common_type<Q, Value> {
+  using type = mp_units::quantity<Q::reference, std::common_type_t<typename Q::rep, Value>>;
+};
+
+template<mp_units::Quantity Q, mp_units::RepresentationOf<mp_units::quantity_character::scalar> Value>
+  requires(Q::unit == mp_units::one) && requires { typename std::common_type_t<typename Q::rep, Value>; }
+struct std::common_type<Value, Q> : std::common_type<Q, Value> {};
diff --git a/test/static/quantity_test.cpp b/test/static/quantity_test.cpp
index 8d3b68f7..d609faea 100644
--- a/test/static/quantity_test.cpp
+++ b/test/static/quantity_test.cpp
@@ -126,9 +126,9 @@ static_assert(quantity<isq::length[m], double>::min().numerical_value_in(m) == s
 static_assert(quantity<isq::length[m], double>::max().numerical_value_in(m) == std::numeric_limits<double>::max());
 
 
-//////////////////////////////
-// construction from a value
-//////////////////////////////
+/////////////////////////////////////////////////
+// no construction from value (unless unit one)
+/////////////////////////////////////////////////
 
 // construction from a value is private
 static_assert(!std::constructible_from<quantity<isq::length[m]>, double>);
@@ -137,11 +137,17 @@ static_assert(!std::convertible_to<double, quantity<isq::length[m]>>);
 static_assert(!std::constructible_from<quantity<isq::length[m], int>, int>);
 static_assert(!std::convertible_to<int, quantity<isq::length[m], int>>);
 
-static_assert(!std::constructible_from<quantity<dimensionless[one]>, double>);
-static_assert(!std::convertible_to<double, quantity<dimensionless[one]>>);
+static_assert(std::constructible_from<quantity<one>, double>);
+static_assert(std::convertible_to<double, quantity<one>>);
 
-static_assert(!std::constructible_from<quantity<dimensionless[one]>, int>);
-static_assert(!std::convertible_to<int, quantity<dimensionless[one]>>);
+static_assert(std::constructible_from<quantity<one>, int>);
+static_assert(std::convertible_to<int, quantity<one>>);
+
+static_assert(std::constructible_from<quantity<dimensionless[one]>, double>);
+static_assert(std::convertible_to<double, quantity<dimensionless[one]>>);
+
+static_assert(std::constructible_from<quantity<dimensionless[one]>, int>);
+static_assert(std::convertible_to<int, quantity<dimensionless[one]>>);
 
 
 ///////////////////////////////////////
@@ -200,6 +206,24 @@ static_assert(quantity<isq::length[km], int>(2 * km).numerical_value_in(km) == 2
 static_assert(quantity<isq::length[km]>(1500 * m).numerical_value_in(km) == 1.5);
 
 
+////////////////////////////////////////////////////////
+// explicit conversion to a number (when unit is one)
+////////////////////////////////////////////////////////
+
+static_assert(!std::convertible_to<quantity<one>, double>);
+static_assert(std::constructible_from<double, quantity<one>>);
+static_assert(!std::convertible_to<quantity<isq::angular_measure[one]>, double>);
+static_assert(std::constructible_from<double, quantity<isq::angular_measure[one]>>);
+static_assert(!std::convertible_to<quantity<one>, int>);
+static_assert(std::constructible_from<int, quantity<one>>);
+static_assert(!std::convertible_to<quantity<isq::angular_measure[one]>, int>);
+static_assert(std::constructible_from<int, quantity<isq::angular_measure[one]>>);
+static_assert(!std::convertible_to<quantity<one, int>, double>);
+static_assert(std::constructible_from<double, quantity<one, int>>);
+static_assert(!std::convertible_to<quantity<isq::angular_measure[one], int>, double>);
+static_assert(std::constructible_from<double, quantity<isq::angular_measure[one], int>>);
+
+
 ///////////////////////////////////
 // converting to a different unit
 ///////////////////////////////////
@@ -320,6 +344,10 @@ static_assert(quantity{123. * m}.unit == si::metre);
 static_assert(quantity{123. * m}.quantity_spec == kind_of<isq::length>);
 static_assert(quantity{123. * h}.unit == si::hour);
 static_assert(quantity{123. * h}.quantity_spec == kind_of<isq::time>);
+static_assert(std::is_same_v<decltype(quantity{123})::rep, int>);
+static_assert(std::is_same_v<decltype(quantity{123.})::rep, double>);
+static_assert(quantity{123}.unit == one);
+static_assert(quantity{123}.quantity_spec == kind_of<dimensionless>);
 
 #if MP_UNITS_HOSTED
 using namespace std::chrono_literals;
@@ -350,6 +378,11 @@ static_assert([]() {
 }()
                 .numerical_value_in(m) == 1);
 
+static_assert([]() {
+  quantity q(1);
+  return q = 2;
+}()
+                .numerical_value_in(one) == 2);
 
 ////////////////////
 // unary operators
@@ -752,6 +785,17 @@ static_assert(4 / (2 * one) == 2 * one);
 static_assert(4 * one / 2 == 2 * one);
 static_assert(4 * one % (2 * one) == 0 * one);
 
+static_assert(1 * one + 1 == 2);
+static_assert(1 + 1 * one == 2);
+static_assert(2 * one - 1 == 1);
+static_assert(2 - 1 * one == 1);
+static_assert(1 * one + 1.23 == 2.23);
+static_assert(1 + 1.23 * one == 2.23);
+static_assert(2.23 * one - 1 == 1.23);
+static_assert(2.23 - 1 * one == 1.23);
+static_assert(4 * one % (2) == 0);
+static_assert(4 % (2 * one) == 0);
+
 static_assert(2 * rad * (2 * rad) == 4 * pow<2>(rad));
 
 // modulo arithmetics
@@ -912,6 +956,9 @@ static_assert(!(123 * km > 321'000 * m));
 static_assert(!(123 * km > 123'000 * m));
 static_assert(!(123 * km >= 321'000 * m));
 
+static_assert(1 * one < 2);
+static_assert(1 < 2 * one);
+
 
 //////////////////
 // dimensionless
@@ -925,6 +972,32 @@ static_assert(50. * m / (100. * m) == 50 * percent);
 static_assert((50. * percent).numerical_value_in(one) == 0.5);
 
 
+//////////////////
+// common_type
+//////////////////
+
+static_assert(
+  is_same_v<std::common_type_t<quantity<isq::speed[m / s], int>, quantity<(isq::length / isq::time)[m / s], double>>,
+            quantity<isq::speed[m / s], double>>);
+static_assert(is_same_v<std::common_type_t<quantity<(isq::mass * pow<2>(isq::length / isq::time))[J], double>,
+                                           quantity<isq::energy[kg * m2 / s2], double>>,
+                        quantity<isq::energy[J], double>>);
+
+#if MP_UNITS_HOSTED
+static_assert(is_same_v<std::common_type_t<quantity<si::second, int>, std::chrono::seconds>, std::chrono::seconds>);
+#endif
+
+static_assert(is_same_v<std::common_type_t<quantity<one, int>, int>, quantity<one, int>>);
+// static_assert(is_same_v<std::common_type_t<quantity<one, int>, double>, quantity<one, double>>);
+// static_assert(is_same_v<std::common_type_t<quantity<one, double>, int>, quantity<one, double>>);
+static_assert(is_same_v<std::common_type_t<quantity<isq::angular_measure[one], int>, int>,
+                        quantity<isq::angular_measure[one], int>>);
+// static_assert(is_same_v<std::common_type_t<quantity<isq::angular_measure[one], int>, double>,
+//                         quantity<isq::angular_measure[one], double>>);
+// static_assert(is_same_v<std::common_type_t<quantity<isq::angular_measure[one], double>, int>,
+//                         quantity<isq::angular_measure[one], double>>);
+
+
 //////////////////
 // value_cast
 //////////////////